Urban areas are increasingly vulnerable to hydrological extreme events, such as pluvial and fluvial floods, which are projected to become more frequent in many parts of the world due to climate change. Addressing these challenges requires cross-disciplinary approaches for sustainable and socio-economically balanced urban water management. This work introduces a technological framework for integrating flood risk management tools into Urban Digital Twins (UDT), focusing on the study area of Dresden, Germany. A 3D UDT web application was developed using geo-topographical and urban infrastructure data, supported by a comprehensive Urban Data Platform (UDP) which stores key inputs for runoff modeling, such as surface roughness and infiltration, enabling the automatic generation of 2D hydro-numeric models and processing pipelines. These integrated flood model utilizes real-time data, 2D-gridded precipitation forecasts or predefined climate scenarios to simulate flood impacts on the city. The results are visualized within the UDT for interactive vulnerability and damage assessments by the users. This framework accelerates decision-making processes, facilitating collaboration between public authorities, scientists, citizens, and industrial partners, while improving urban planning and flood resilience in the context of climate change.